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Mean Balance

Age 11 to 14 Short Challenge Level:

The mean of the set of numbers 8, 4, 5, 4,  and 6 is 6.

If another  is added to the set, then the mean is still 6.

What numbers do  and  represent?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.